Perfect Pai Gow hand

Just wondering - what pai Gow hand will win more then loose or tie? A straight or flush is a great 5 card hand but would loose the 2 card hand. I saw this in Atlantic city where a player had a straight Ace high but had 2-8 on his 2 card hand and thus a push. It seem to me that 2 small pairs win more then 50% of the time. Thoughts?

AAAA*KK
In other words, five Aces and a pair of Kings..unbeatable hand.

AKQ*10 AA
Royal flush with a pair of aces

Quote: jdominik

Just wondering - what pai Gow hand will win more then loose or tie? A straight or flush is a great 5 card hand but would loose the 2 card hand. I saw this in Atlantic city where a player had a straight Ace high but had 2-8 on his 2 card hand and thus a push. It seem to me that 2 small pairs win more then 50% of the time. Thoughts?

Generally an average high hand is a pair of 9's. An average low hand is KQ

IIRC, I read somewhere that Sanford Wong's book says the magic hand is a pair of jacks with an A/8 up.

I'm not really sure what the OP's question is, but I stumbled across a conundrum while thinking about it.

I assert that it is impossible to devise a hand which has the same probability of winning, losing and tying. This does not seem intuitively obvious to me, but it seems to be the way the math works.

If the probability of the front hand winning is x, and the probability of the back hand winning is y, then the overall probabilities are:

win: x*y
lose: (1-x)*(1-y)
tie: (1-x)*y + (1-y)*x or 1 - x*y - (1-x)*(1-y)

For win=lose=tie=0.333, I think I determine that x and y must be imaginary. Seems weird to me.

Quote: PapaChubby

... tie: (1-x)*y + (1-y)*x or 1 - x*y - (1-x)*(1-y) ...

I think you made an algebra/multiplication error on that line. But the solution does appear to involve complex values of x and y.

Quote: PGBuster

IIRC, I read somewhere that Sanford Wong's book says the magic hand is a pair of jacks with an A/8 up.

PG - that's the "median" hand or average hand. The dead Center hand.

Quote: clarkacal

AKQ*10 AA
Royal flush with a pair of aces

Correct, best hand, Royal with Aces on top.

The AAAA*/KK hand could indeed push: dealer could have three pairs 66552/KK, and win the two-side copy KK (Dealer wins copies on each side.)

Quote: clarkacal

AKQ*10 AA
Royal flush with a pair of aces

This is unbeatable, but wouldn't it push against the dealer's suited AKQJ10 XY, since the dealer's copied royal flush would beat the player's royal flush?